To me the martian was from a time when Martian society was at its height, while the man was from the present. A weird time slip brought them both to the same time period, and only lasted a few moments.

I remember this question from when it was first posted and I liked it, but was not sure I could sufficiently explain what I thought Bradbury was saying. I also thought it was a bit egotistical to think I could explain what he was thinking at the time.

For me at least it was something of a study in relativism. We all have our own reality. And each reality is as valid as the next in a given situation. For the two individuals in the story, each had his reality and each functioned within that. Both were right for himself. Both were invalid for the other.

Bradbury deliberately raises ambiguity about the Martian. Is he an ancestor of the Martian natives who were exterminated by earthly diseases? Or is he a descendant of the Earth colonists who survived on Mars after the nuclear war exterminated life on Earth? Is he a ghost of the past, or a vision of the future? Or is it an endless circle, with each planet rising, colonizing the other, then falling?

Each man lives in his civilization at the height of its power, and each man has difficulty imagining that it could end. Each man believes that he is alive in the present, and that the other is a ghost of the dead past. Which one is right? How can anyone be certain? And, since each man is mortal, and each civilization is mortal, does it really matter?